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We prove that any linear multi-step method Gτ1 of the form m∑k=0αkZk=τm∑k=0βkJ-1(△)H(Zk) with odd order u (u ≥ 3) cannot be conjugate to a symplectic method Gτ2 of order w(w ≥ u) via any generalized linear multi-step method Gτ3 of the form m∑k=0αkZk=τm∑k=0βkJ-1(△)H(m∑l=0γklZl).We also give a necessary condition for this kind of generalized linear multi-step methods to be conjugate-symplectic. We also demonstrate that these results can be easily extended to the case when Gτ3 is a more general operator.